Skip to main content
SpringerLink
Log in
Book cover

International Symposium on Algorithmic Game Theory

SAGT 2010: Algorithmic Game Theory pp 1–14Cite as

When the Players Are Not Expectation Maximizers

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 6386))

Abstract

Much of Game Theory, including the Nash equilibrium concept, is based on the assumption that players are expectation maximizers. It is known that if players are risk averse, games may no longer have Nash equilibria [11,6]. We show that

  1. 1

    Under risk aversion (convex risk valuations), and for almost all games, there are no mixed Nash equilibria, and thus either there is a pure equilibrium or there are no equilibria at all, and,

  2. 1

    For a variety of important valuations other than expectation, it is NP-complete to determine if games between such players have a Nash equilibrium.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Allais, M.: Le comportement de l’homme rationnel devant le risque: Critique des postulats et axiomes de l’ecole americaine. Econometrica 21(4), 503–546 (1953), http://www.jstor.org/stable/1907921

    Article  MathSciNet  MATH  Google Scholar 

  2. Bernoulli, D.: Exposition of a new theory on the measurement of risk. Commentaries of the Imperial Academy of Science of Saint Petersburg (1738); Republished Econometrica 22(1), 23–36 (1954), http://www.jstor.org/stable/1909829

  3. Borel, E.: The theory of play and integral equations with skew symmetric kernels. In: Translated by Leonard J. Savage, University of Chicago, from Comptes Rendus de l’Academie des Sciences, December 19, vol. 173, pp. 1304–1308 (1921); Reprinted in Econometrica 21(1), 97–100 (1953), http://www.jstor.org/stable/1906946

  4. Chen, X., Deng, X.: Settling the complexity of two-player nash equilibrium. In: FOCS 2006: Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science, pp. 261–272. IEEE Computer Society, Washington (2006)

    Chapter  Google Scholar 

  5. Conitzer, V., Sandholm, T.: New complexity results about nash equilibria. Games and Economic Behavior 63(2), 621–641 (2008), http://econpapers.repec.org/RePEc:eee:gamebe:v:63:y:2008:i:2:p:621-641

    Article  MathSciNet  MATH  Google Scholar 

  6. Crawford, V.P.: Equilibrium without independence. Journal of Economic Theory 50(1), 127–154 (1990), http://www.sciencedirect.com/science/article/B6WJ3-4CYH5N4-CF/2/0071841ad1283474807beca912feb550

    Article  MathSciNet  MATH  Google Scholar 

  7. Daskalakis, C., Goldberg, P.W., Papadimitriou, C.H.: The complexity of computing a nash equilibrium. ACM Commun. 52(2), 89–97 (2009)

    Article  MATH  Google Scholar 

  8. Friedman, M., Savage, L.J.: The utility analysis of choices involving risk. Journal of Political Economy 56 (1948), http://econpapers.repec.org/RePEc:ucp:jpolec:v:56:y:1948:p:279

  9. Chen, H.-C.: Pure-strategy equilibria with non-expected utility players. Theory and Decision 46, 201–212 (1999), http://www.ingentaconnect.com/content/klu/theo/1999/00000046/00000002/00152924

    Article  MathSciNet  Google Scholar 

  10. Kahneman, D., Tversky, A.: Prospect theory: An analysis of decision under risk. Econometrica 47(2), 263–291 (1979), http://www.jstor.org/stable/1914185

    Article  MATH  Google Scholar 

  11. Karni, E., Safra, Z.: Dynamic consistency, revelations in auctions and the structure of preferences. Review of Economic Studies 56(3), 421–433 (1989), http://econpapers.repec.org/RePEc:bla:restud:v:56:y:1989:i:3:p:421-33

    Article  MathSciNet  MATH  Google Scholar 

  12. Machina, M.J.: Choice under uncertainty: Problems solved and unsolved. The Journal of Economic Perspectives 1(1), 121–154 (1987), http://www.jstor.org/stable/1942952

    Article  Google Scholar 

  13. Machina, M.J.: Dynamic consistency and non-expected utility models of choice under uncertainty. Journal of Economic Literature 27(4), 1622–1668 (1989), http://ideas.repec.org/a/aea/jeclit/v27y1989i4p1622-68.html

    Google Scholar 

  14. Markowitz, H.: Portfolio Selection: Efficient Diversification in Investments. John Wiley, Chichester (1959)

    Google Scholar 

  15. Markowitz, H.: Portfolio selection. The Journal of Finance 7(1), 77–91 (1952), http://www.jstor.org/stable/2975974

    Google Scholar 

  16. Marschak, J.: Rational behavior, uncertain prospects, and measurable utility. Econometrica 18(2), 111–141 (1950), http://www.jstor.org/stable/1907264

    Article  MathSciNet  MATH  Google Scholar 

  17. Myerson, R.B., Myerson, R.B.: Nash equilibrium and the history of economic theory. Journal of Economic Literature 37, 1067–1082 (1999)

    Article  Google Scholar 

  18. Nash, J.: Non-cooperative games. The Annals of Mathematics 54(2), 286–295 (1951), http://www.jstor.org/stable/1969529

    Article  MathSciNet  MATH  Google Scholar 

  19. Neumann, J.v.: Zur Theorie der Gesellschaftsspiele. Math. Ann. 100(1), 295–320 (1928), http://dx.doi.org/10.1007/BF01448847

    Article  MathSciNet  MATH  Google Scholar 

  20. Neumann, J.V., Morgenstern, O.: Theory of Games and Economic Behavior. Princeton University Press, Princeton (1944), http://jmvidal.cse.sc.edu/library/neumann44a.pdf

    MATH  Google Scholar 

  21. Papadimitriou, C.H.: On the complexity of the parity argument and other inefficient proofs of existence. J. Comput. Syst. Sci. 48(3), 498–532 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  22. Translated by Richard J. Pulskamp, N.B.: Correspondence of nicolas bernoulli concerning the st. petersburg game (1713-1732) (1999), http://cerebro.xu.edu/math/sources/montmort/stpetersburg.pdf

  23. Ritzberger, K.: On games under expected utility with rank dependent probabilities. Theory and Decision 40(1), 1–27 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  24. Sharpe, W.F.: A simplified model for portfolio analysis. Management Science 9(2), 277–293 (1963), http://www.jstor.org/stable/2627407

    Article  Google Scholar 

  25. Stanford, W.: The limit distribution of pure strategy nash equilibria in symmetric bimatrix games. Mathematics of Operations Research 21(3), 726–733 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  26. Starmer, C.: Developments in non-expected utility theory: The hunt for a descriptive theory of choice under risk. Journal of Economic Literature 38(2), 332–382 (2000), http://ideas.repec.org/a/aea/jeclit/v38y2000i2p332-382.html

    Article  Google Scholar 

  27. Varian, H.: A portfolio of nobel laureates: Markowitz, miller and sharpe. The Journal of Economic Perspectives 7(1), 159–169 (1993), http://www.jstor.org/stable/2138327

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Computer Science, Tel Aviv University, Israel

    Amos Fiat

  2. Computer Science Division, University of California at Berkeley, USA

    Christos Papadimitriou

Authors
  1. Amos Fiat
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Christos Papadimitriou
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Lecturer, Department of Computer Science, University of Ioannina, Dourouti University Campus, 45110, Ioannina, Greece

    Spyros Kontogiannis

  2. Department of Informatics and Telecommunications Panepistimiopolis, Ilissia, Professor, National and Kapodistrian University of Athens, 15784, Athens, Greece

    Elias Koutsoupias

  3. Computer Engineering and Informatics Department (CEID), University of Patras, 26500, Patras, Greece

    Paul G. Spirakis

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Fiat, A., Papadimitriou, C. (2010). When the Players Are Not Expectation Maximizers. In: Kontogiannis, S., Koutsoupias, E., Spirakis, P.G. (eds) Algorithmic Game Theory. SAGT 2010. Lecture Notes in Computer Science, vol 6386. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16170-4_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-16170-4_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-16169-8

  • Online ISBN: 978-3-642-16170-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation